After the aperture, a rotator lens follows (Fig. REF (a), orange). In order to preserve the location of the focal planes behind the rotator lens, it is embedded between two electrostatic lenses (Fig. REF (a), green), which form a focal spot located in the center of the rotator lens. Thus, the trajectories of the electron beam are all center rays of the rotator lens, greatly unaffected by changes of its magnetic excitation. Transverse polarization components of \(\mathbf {P}\)  precess around the axial field (\(\mathbf {B_2}\) ) of the rotator lens [1]} with an axial rotation defined as \(\Phi \) . The Larmor precession of the electron enables either left- or right-handed rotations whose magnitude depends on both the current in the rotator solenoid and the rotator lens potential. The rotator potential is set to maximize the transmitted current onto the target alongside a tight focusing of the beam. Both conditions were experimentally explored by means of the heuristic Nelder-Mead (NM) method [2]}. The NM method provided with optimized voltages on the rotator for maximizing the electron transmission by using the current in the rotator coils as a dependent parameter. Fig. REF  exhibits the electron transmission as a function of the current and the voltage of the rotator for a beam of 10 eV. The symmetry of the rotator voltage, with respect to the initial condition (\(\mathbf {B_2}=\mathbf {0}\) ), and the parameters for a maximum transmission to the target are both evidenced.
